Nash Bargaining for Log-Convex Problems

36 Pages Posted: 16 Jan 2015

See all articles by Cheng-Zhong Qin

Cheng-Zhong Qin

University of California, Santa Barbara (UCSB) - Department of Economics

Shuzhong Shi

Peking University (Deceased)

Guofu Tan

University of Southern California - Department of Economics

Date Written: December 3, 2014

Abstract

We introduce log-convexity for bargaining problems. With the requirement of some basic regularity conditions, log-convexity is shown to be necessary and sufficient for Nash's axioms to determine a unique single-valued bargaining solution up to choices of bargaining powers. Specifically, we show that the single-valued (asymmetric) Nash solution is the unique solution under Nash's axioms without that of symmetry on the class of all regular and log-convex bargaining problems, but this is not true on any larger class. We apply our results to bargaining problems arising from duopoly and the theory of the firm. These problems turn out to be log-convex but not convex under familiar conditions. We compare the Nash solution for log-convex bargaining problems with some of its extensions in the literature.

Keywords: Bargaining problem, Non-convexity, Log-convexity, Nash solution, Nash product

JEL Classification: C78, D21, D43

Suggested Citation

Qin, Cheng-Zhong and Shi, Shuzhong and Tan, Guofu, Nash Bargaining for Log-Convex Problems (December 3, 2014). USC-INET Research Paper No. 15-04, Available at SSRN: https://ssrn.com/abstract=2550016 or http://dx.doi.org/10.2139/ssrn.2550016

Cheng-Zhong Qin (Contact Author)

University of California, Santa Barbara (UCSB) - Department of Economics ( email )

2127 North Hall
Santa Barbara, CA 93106
United States

Shuzhong Shi

Peking University (Deceased)

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Guofu Tan

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave. Kaprielian (KAP) Hall, 300
Los Angeles, CA 90089
United States
213-740-3520 (Phone)

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